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Chengchun Hao's Publications

PUBLICATIONS

My papers in ResearchGate, arXiv, MathSciNet, Google Scholar, ORCID

Preprints

  1. Wei Zhang, Jie Fu and Chengchun Hao
    On the finite-time splash singularity for the free-boundary problem of 3d incompressible neo-Hookean elastodynamics NEW
    In preparation , 2025. bib
  2. Chengchun Hao, Tao Luo and Siqi Yang
    Classification of finite-time blow-up of strong solutions to the incompressible free boundary Euler equations with surface tension NEW
  3. Wei Zhang, Jie Fu, Chengchun Hao and Siqi Yang
    Global well-posedness of the free boundary problem for incompressible viscous resistive MHD in critical Besov spaces

    Books or Lectures

    • 郝成春现代实分析讲义完善中,2024.
    • 郝成春、 杨思奇, 实分析讲义完善中,2023.
    • Chengchun Hao, Introduction to Harmonic Analysis (调和分析导论讲义, 英文版), 拟出版,2024. 目录
    • Baoxiang Wang, Zhaohui Huo, Chengchun Hao and Zihua Guo
      Harmonic Analysis Method for Nonlinear Evolution Equations,I, 已出版, 2011 World Scientific Pub Co Inc 300pp.
      ——中文版: 非线性发展方程的调和分析方法, (I)适定性理论 未出版, 2010 PDF

    Published or Accepted Papers

    ■ Free boundary problems in fluid dynamics equations

    ♣ MHD equations
  1. Chengchun Hao and Siqi Yang
    A priori estimates and a blow-up criterion for the incompressible ideal MHD equations with surface tension and a closed free surface NEW
    Nonlinearity38(7): 075009 (47pp), 2025. PDFarXiv:2312.09473DOI bib
  2. Chengchun Hao and Siqi Yang
    On a regularity criterion for free boundary incompressible ideal MHD with surface tension NEW
    Accepted Communications in Information and Systems25: 18pp, 2025. bib
  3. Chengchun Hao and Siqi Yang
    Splash singularity for the free boundary incompressible viscous MHD
    Journal of Differential Equations379: 26–103, 2024. PDFarXiv:2304.06893DOI bib
  4. Jie Fu, Chengchun Hao, Siqi Yang and Wei Zhang
    A Beale-Kato-Majda criterion for free boundary incompressible ideal magnetohydrodynamics
    Journal of Mathematical Physics64(9): 091505 (16pp), 2023. PDFDOI bib
  5. Chengchun Hao and Wei Zhang
    A priori estimates for free boundary problem of 3D incompressible inviscid rotating Boussinesq equations
    Zeitschrift für angewandte Mathematik und Physik74(2): 80 (21pp), 2023. PDFDOI bib
  6. Chengchun Hao and Tao Luo
    Some results on free boundary problems of incompressible ideal magnetohydrodynamics equations
    Electronic Research Archive30(2): 404-424, 2022. PDFDOI bib
  7. Chengchun Hao and Tao Luo
    Well-posedness for the linearized free boundary problem of incompressible ideal magnetohydrodynamics equations
    Journal of Differential Equations299: 542-601, 2021. PDFarXiv:1912.05908DOI bib
  8. Chengchun Hao and Tao Luo
    Ill-posedness of free boundary problem of the incompressible ideal MHD
    Communications in Mathematical Physics376(1): 259–286, 2020. PDFarXiv:1810.07465DOI bib
  9. Chengchun Hao
    On the motion of free interface in ideal incompressible MHD
    Archive for Rational Mechanics and Analysis224(2): 515–553, 2017. PDFarXiv:1607.02731DOI bib
  10. Chengchun Hao and Tao Luo
    A priori estimates for free boundary problem of incompressible inviscid magnetohydrodynamic flows
    Archive for Rational Mechanics and Analysis212(3): 805-847, 2014. PDFarXiv:1301.7123DOI bib

  11. ♣ Two-phase equations
  12. Chengchun Hao, Tao Luo and Siqi Yang
    Exponential stability of a free boundary problem with spherical symmetry for a gas bubble immersed in a bounded incompressible liquid NEW
    Calculus of Variations and Partial Differential Equations64: 207 (45pp), 2025. PDFarXiv:2408.15587DOI bib
  13. Wei Zhang, Jie Fu, Chengchun Hao and Siqi Yang
    Global well-posedness for two-phase fluid motion in the Oberbeck-Boussinesq approximation
    Journal of Mathematical Physics65(8): 081509 (22pp), 2024. PDFDOI bib
  14. Chengchun Hao and Wei Zhang
    Local well-posedness for two-phase fluid motion in the Oberbeck-Boussinesq approximation
    Communications on Pure and Applied Analysis22(7): 2099-2131, 2023. PDFDOI bib
  15. Chengchun Hao and Wei Zhang
    Maximal $ L^p$-$ L^q$ regularity for two-phase fluid motion in the linearized Oberbeck-Boussinesq approximation
    Journal of Differential Equations322: 101-134, 2022. PDFDOI bib

  16. ♣ Elastodynamics
  17. Jie Fu, Chengchun Hao, Siqi Yang and Wei Zhang
    不可压新Hooke 型弹性动力学自由边界问题的爆破准则 NEW
    中国科学:数学55(3): 635-650, 2025. PDFDOI bib
  18. Chengchun Hao and Dehua Wang
    A priori estimates for the free boundary problem of incompressible neo-Hookean elastodynamics
    Journal of Differential Equations261(1): 712–737, 2016. PDFDOI bib

  19. ♣ Euler equations
  20. Chengchun Hao
    Remarks on the free boundary problem of compressible Euler equations in physical vacuum with general initial densities
    Discrete and Continuous Dynamical Systems - B20(9): 2885-2931, 2015. PDFarXiv:1301.7121DOI bib

  21. ■ Well-posedness of Cauchy problems to fluid dynamics equations

  22. Chengchun Hao and Hai-Liang Li
    Well-posedness for a multidimensional viscous liquid-gas two-phase flow model
    SIAM Journal on Mathematical Analysis44(3): 1304–1332, 2012. PDFarXiv:1107.4179DOI bib
  23. Chengchun Hao
    Global well-posedness for a multidimensional chemotaxis model in critical Besov spaces
    Zeitschrift für angewandte Mathematik und Physik63(5): 825-834, 2012. PDFDOI bib
  24. Yiquan Lin, Chengchun Hao and Hai-Liang Li
    Global well-posedness of compressible bipolar Navier-Stokes-Poisson equations
    Acta Mathematica Sinica, English Series28(5): 925-940, 2012. PDFDOI bib
  25. Chengchun Hao
    Well-posedness for the viscous rotating shallow water equations with friction terms
    J. Math. Phys.52(2): No.023101, 12pp, 2011. PDFDOI bib
  26. Chengchun Hao
    Well-posedness to the compressible viscous magnetohydrodynamic system
    Nonlinear Analysis: Real World Applications12(6): 2962–2972, 2011. PDFDOI bib
  27. Chengchun Hao
    Cauchy problem for viscous shallow water equations with surface tension
    Discrete Contin. Dyn. Syst. Ser. B13(3): 593-608, 2010. PDFDOI bib
    We are concerned with the Cauchy problem for a viscous shallow water system with a third-order surface-tension term. The global existence and uniqueness of the solution in the space of Besov type is shown for the initial data close to a constant equilibrium state away from the vacuum by using the Friedrich's regularization and compactness arguments.
  28. Chengchun Hao, Ling Hsiao and Hai-Liang Li
    Cauchy problem for viscous rotating shallow water equations
    Journal of Differential Equations247(12): 3234–3257, 2009. PDFDOI bib
  29. Chengchun Hao and Hai-Liang Li
    Global existence for compressible Navier–Stokes–Poisson equations in three and higher dimensions
    Journal of Differential Equations246(12): 4791–4812, 2009. PDFDOI bib

  30. ■ Well-posedness of IVP/IBVP to dispersive equations

  31. Recent progress on some kinds of nonlinear dispersive partial differential equations (in Chinese)
    Research Series for Excellent Doctoral Dissertation of Chinese Academy of Sciences vol. 2007, 1-6, Science Press, Beijing, 2008.
  32. Chengchun Hao, Ling Hsiao and Hai-Liang Li
    Global well posedness for the Gross–Pitaevskii equation with an angular momentum rotational term
    Math. Methods Appl. Sci.31(6): 655-664, 2008. PDFDOI bib
  33. Chengchun Hao, Ling Hsiao and Hai-Liang Li
    Global well posedness for the Gross-Pitaevskii equation with an angular momentum rotational term in three dimensions
    J. Math. Phys.48(10): No.102105, 11pp, 2007. PDFDOI bib
  34. Chengchun Hao
    Well-posedness for one-dimensional derivative nonlinear Schrödinger equations
    Commun. Pure Appl. Anal.6(4): 997-1021, 2007. PDFDOI bib
  35. Chengchun Hao, Ling Hsiao and Baoxiang Wang
    Well-posedness of Cauchy problem for the fourth order nonlinear Schrödinger equations in multi-dimensional spaces
    Journal of Mathematical Analysis and Applications328(1): 58-83, 2007. PDFDOI bib
  36. Chengchun Hao, Ling Hsiao and Baoxiang Wang
    Wellposedness for the fourth order nonlinear Schrödinger equations
    Journal of Mathematical Analysis and Applications320(1): 246-265, 2006. PDFDOI bib
  37. Baoxiang Wang, Chengchun Hao and Henryk Hudzik
    Energy scattering theory for the nonlinear Schrödinger equations with exponential growth in lower spatial dimensions
    Journal of Differential Equations228(1): 311-338, 2006. PDFDOI bib
  38. Chengchun Hao
    The initial boundary value problem for quasi-linear Schrödinger-Poisson equations
    Acta Math. Sci. Ser. B Engl. Ed.26(1): 115-124, 2006. PDFDOI bib
  39. Chengchun Hao and Ling Hsiao
    Studies on Schrödinger-Poisson systems (Excerpt of Dissertation)
    J. Grad. Sch. of CAS22(5): 141-146, 2005. bib
  40. Chengchun Hao and Hai-Liang Li
    On the initial value problem for the bipolar Schrödinger-Poisson systems
    J. Partial Diff. Eqns.17(3): 283-288, 2004. PDFbib
  41. Chengchun Hao, Ling Hsiao and Hai-Liang Li
    Modified scattering for bipolar nonlinear Schrödinger-Poisson equations
    Math. Models Methods Appl. Sci.14(10): 1481-1494, 2004. PDFDOI bib
  42. Chengchun Hao and Ling Hsiao
    Large time behavior and global existence of solution to the bipolar defocusing nonlinear Schrödinger-Poisson system
    Quart. Appl. Math.62(4): 701-710, 2004. PDFDOI bib
  43. Chengchun Hao
    Energy scattering for the generalized Davey-Stewartson equations
    Acta Mathematicae Applicatae Sinica, English Series19(2): 333-340, 2003. PDFDOI bib
  44. Chengchun Hao
    Energy Scattering for Nonlinear Davey-Stewartson Equations
    Journal of Mathematical Research and Exposition23(4): 645-650, 2003. bib
  45. Chengchun Hao
    Energy scattering for the generalized Davey-Stewartson equations (科技创新快报)
    Journal of Hebei University (Natural Science Edition)22(1): 73-74, 2002. bib
  46. Energy scattering for nonlinear Davey-Stewartson equations (in Chinese)
    J. Math. Res. Expo. 23(4), 645-650, 2003.   
  47. Energy scattering for the generalized Davey-Stewartson equations (Rapid Communications)
    Hebei Uni., Rat. Sci. Edt. 22(1), 73-74, 2002.

  48. ■ Well-posedness or asymptotic of IVP/IBVP to quantum models

  49. Hai-Liang Li, Guo-Jing Zhang, Min Zhang and Chengchun Hao
    Long-time self-similar asymptotic of the macroscopic quantum models
    J. Math. Phys.49(7): No.073503, 14pp, 2008. PDFDOI bib
  50. Chengchun Hao, Yueling Jia and Hai-Liang Li
    Quantum Euler-Poisson system: local existence of solutions
    J. Partial Diff. Eqns.16(4): 306-320, 2003. PDFbib